EP2891268B1 - Gruppensignatur unter verwendung eines pseudonyms - Google Patents

Gruppensignatur unter verwendung eines pseudonyms Download PDF

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Publication number
EP2891268B1
EP2891268B1 EP14712007.5A EP14712007A EP2891268B1 EP 2891268 B1 EP2891268 B1 EP 2891268B1 EP 14712007 A EP14712007 A EP 14712007A EP 2891268 B1 EP2891268 B1 EP 2891268B1
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Prior art keywords
signature
pseudonym
group
key
domain
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English (en)
French (fr)
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EP2891268A1 (de
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Alain PATEY
Hervé Chabanne
Julien Bringer
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Idemia Identity and Security France SAS
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Safran Identity and Security SAS
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • H04L9/3255—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using group based signatures, e.g. ring or threshold signatures
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/08—Network architectures or network communication protocols for network security for authentication of entities
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3218—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using proof of knowledge, e.g. Fiat-Shamir, GQ, Schnorr, ornon-interactive zero-knowledge proofs
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3263—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving certificates, e.g. public key certificate [PKC] or attribute certificate [AC]; Public key infrastructure [PKI] arrangements
    • H04L9/3268—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving certificates, e.g. public key certificate [PKC] or attribute certificate [AC]; Public key infrastructure [PKI] arrangements using certificate validation, registration, distribution or revocation, e.g. certificate revocation list [CRL]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/42—Anonymization, e.g. involving pseudonyms

Definitions

  • the present invention generally relates to the field of digital signatures.
  • the invention more specifically relates to a new signature method combining a group signature with the use of pseudonyms, for authentication purposes.
  • identity documents such as machine readable travel documents (MRTDs ) such as passports or identity cards.
  • MRTDs machine readable travel documents
  • a connection is established between the identity document and a terminal T of the service provider and various security mechanisms are put in place.
  • PACE Password Authenticated Connection Establishment
  • EAC Extended Access Control
  • the Restricted Identification (RI) protocol makes it possible to generate a pseudonym specific to an identity document for a given domain grouping a set of terminals of the service provider. This pseudonym allows said terminals to identify the identity document. Moreover, this protocol satisfies the property of "cross-domain anonymity": it is impossible to establish a link between the pseudonyms used for different domains for the same document of identity.
  • This protocol can be extended to use such pseudonyms to digitally sign a message.
  • Such a variant of this protocol is described in the reference Bender, J., Dagdelen, O., Fischlin, M., Kugler, D .: Domain-specific pseudonymous signatures for the German identity card.
  • This protocol ensures that the user has a valid and unrevoked signing key, and that the pseudonym used is legitimate.
  • this protocol is based on the assumption that users can not recover their signature key, this key being supposed to be stored on an inviolable chip of an identity document. Indeed, the pooling by at least two users of their signature keys would allow them to find the secret key of the key management authority and thus generate new valid keys. There is therefore a need to provide a secure signature mechanism even in case of recovery and sharing of the signature keys of multiple users.
  • this protocol also assumes that the key management authority does not store the signature keys generated for the users, once they are delivered. Indeed, the knowledge of keys by the key management authority would allow it to use them to sign a message in place of any legitimate user. However, the lack of memorization of these keys by the key management authority is difficult to guarantee. There is therefore also a need to provide a signature mechanism to ensure that no authority can sign a message in place of a user.
  • the signing of a message or challenge by a member with his secret key allows him to prove that he is a member of the group while remaining anonymous.
  • the subject of the invention is a method for signing a message m implemented by means for processing a user device of a member M i belonging to a group of members managed by a key management authority, said user device holding a secret ski signature key, comprising a generation step for the message m of a group signature ⁇ enabling said member M i to prove membership in the group of members and an step of generating a pseudonym nym ij identifying the member M i in a domain D j of a service provider SP j , said domain D j comprising a set of terminals in communication with a server of said service provider, said signature ⁇ being constructed so that said Mi member can prove by signing the message m his knowledge of said secret signature key without disclosing it, and characterized in that said group signature is constructed such that membership of the member in the group is verifiable independently of the pseudonym, and in that the secret signature key sk i of the member M i comprises at least a first key portion f
  • the signature mechanism of the invention thus combines a group signature and the use of pseudonyms, and allows the signer to prove his membership in the group while having an identity in this group.
  • said secret signature key (ski) is stored in a secure storage means to prevent access to it by a third party.
  • said method may comprise a key generation step implemented by a key management server of the management authority of keys, during which, management server processing means generate for the group of members a set of public parameters gpk, determine a domain parameter dpk j specific to the domain D j , and transmit this parameter to the service provider SP j .
  • the domain parameter (dpk j ) is equal to g 1 rj , where r j is an integer and g1 is a generator of a group G1, where g1 is a parameter among the set of public parameters (gpk).
  • the integer r j is determined by the key management authority.
  • said nym ij pseudonym of the member M i in the domain D j is a function of domain parameter dpk j specific to the domain D j determined by said management server.
  • the pseudonym nym ij may be equal to dpk j xi with xi said second secret signature key portion of the member M i and dpk j said domain parameter.
  • the pseudonym of a member is different in each domain and does not reveal the secret key part used to generate it, which makes it possible to guarantee that pseudonyms of the same member in two different domains can not be linked.
  • said signature ⁇ can comprise a value K, different from the pseudonym, of the form B ⁇ xi with B an element of a group G1 and xi said second secret signature key part of the member M i .
  • the user device processing means implement a zero-knowledge proof proof algorithm in which said signature is generated so as to prove that the member identified by the pseudonym (nim ij ) is the signatory of the message.
  • a null disclosure algorithm allows the signer to provide proof of his identity without disclosing his secret key.
  • the subject of the invention is also a method for controlling a signature of a message m and a pseudonym implemented by means of processing a control server, said signature ⁇ and said pseudonym nymij being generated according to the signature method described above, comprising a verification step, based on the signature ⁇ and the pseudonym nymij, of the knowledge by the member Mi of the ski signature secret key and that said pseudonym and said signature of the member Mi depend on a second part xi of said secret signature key, so as to prove that the member identified by the pseudonym is the signatory of the message m and that it belongs to the group of members ;
  • said verification step comprises a proof verification step in which the control server processing means verifies that a zero-disclosure proof of knowledge proving that the member identified by the pseudonym is the signatory of the message (m ) is correct.
  • Said proof verification step can verify the equality of the discrete logarithms of the value K in base B and the pseudonym nym ij in base dpk j . Such a step thus proves that the member identified by the pseudonym is indeed the signatory of the message m without having to calculate said discrete logarithms and without revealing any part of the secret signature key of the member M i .
  • said verification step comprises a verification of said signature to prove the membership of the member (Mi) to the group and said proof verification step is performed during the verification of said signature.
  • the verification of the signature makes it possible both to prove the signatory's belonging to the group and to prove that the member identified by the pseudonym is indeed the signatory of the message.
  • the control method may also include a step of checking the revocation of the member's member's Mi member .
  • control server processing means can verify in a database that the nym pseudonym ij of the member Mi does not belong to a revocation list RL j for the domain D j , said revocation list being constructed from the pseudonyms nym ij members of the group revoked by the managing authority.
  • the managing authority wishing to dismiss the group of members a member Mi transmits said second secret key portion x i of the member M i to the supplier Service SP j .
  • the revocation list RL j for the domain D j stored in a database is constructed by the service provider SP j by adding in the revocation list RL j , the pseudonym nym ij of the member Mi calculated from said second part secret key received.
  • the invention also relates to a computer program comprising program code instructions for executing the steps of the signature and signature control methods defined above when said program is executed on a computer, a user device and a control server comprising at least one storage means, a processing means and a communication interface configured to respectively implement a signature method and a signature control method as defined above as well as a system comprising at least one such user device and at least one such control server.
  • the figure 2 represents an example of a system for implementing the methods according to the invention.
  • Such a system includes a set of user devices 201 each owned by a member Mi, (i integer) belonging to a set of members constituting a group of members , reader terminals 202, a key management authority 203, service providers 204 and auditors 205, the verifiers may be service providers.
  • the set of user devices, the reading terminals, the key management authority, the service providers and the verifiers are interconnected via a computer network 206.
  • a set of terminals of this network in communication with a network is provided.
  • service provider is a domain.
  • the key management authority, the service providers and the verifiers can be connected to this network by respective servers comprising a random access memory and storage means such as a rewritable non-volatile memory (flash memory or EEPROM) which can storing a database, processing means comprising a processor, cryptographic units for generating particular random numbers, etc ... and interface means allowing them to communicate with other entities on the network and to be connected to databases.
  • servers may also include input and user interface means for their administration.
  • the servers of the above-mentioned entities are respectively called key management server 203s, service provider server 204s, and control server 205s in the remainder of the description.
  • At least two of these servers can be brought together in a single computer device jointly ensuring the functions of said servers.
  • the user device of a member M i may comprise a portable electronic device capable of storing secure data readable by a reading terminal.
  • a portable electronic device may be an identity document comprising a chip in which secure data is stored, for example a machine readable travel document (MRTD ) such as a passport or an identity card, a flash memory storage device provided with a USB communication interface, called a USB key ("Universal Serial Bus"), a smart card, etc.
  • the portable electronic device may comprise a random access memory and storage means such as a non-volatile memory rewritable (flash memory or EEPROM memory), processing means comprising a processor, cryptographic units for generating particular random numbers etc ...
  • the portable electronic device may also include a contactless communication interface such as an RFID or NFC interface, or a wireless communication interface such as a Bluetooth or Wifi interface.
  • the secure data stored in the portable electronic device can be biometric data.
  • the portable device can be provided with sensors for capturing the biometric data of a member Mi, such as fingerprints, palm or retinal.
  • a portable electronic device and a reading terminal may communicate via wireless or non-contact communications such as those mentioned above. They can also communicate through a USB interface, Firewire or any other wired communication interface. They can also communicate through an ISO 7816 smart card contact interface.
  • a reading terminal may also include a wired or wireless communication interface adapted for connecting the terminal to the computer network, such as an Ethernet, Wifi or 3G interface; and a user interface allowing the member M i to control its operation.
  • a wired or wireless communication interface adapted for connecting the terminal to the computer network, such as an Ethernet, Wifi or 3G interface; and a user interface allowing the member M i to control its operation.
  • a portable electronic device and a reading terminal can be joined together in the same electronic device comprising communication interface and user interface means similar to those described above.
  • the network connecting the M i members and the servers consists for example in an Ethernet local area network, a wireless local area network, the Internet network, a mobile telephone network ...
  • the communications on this network are secure, in particular by encrypting the exchanged data.
  • the figure 3 represents a flowchart illustrating the generic steps of the signature method in an embodiment of the invention.
  • the signature mechanism of the invention combines a group signature and the use of pseudonyms.
  • the presented group signature mechanism is based on a VLR ("Verifier Local Revocation") group signature mechanism as described in reference Bringer J., Patey A .: VLR group signatures - how to achieve both backward unlinkability and efficient revocation checks. In: SECRYPT. pp. 215-220 (2012 ).
  • the signature method according to the invention may comprise a key generation step E100, a group membership step E200 and a signature step E300, described in the following paragraphs.
  • the notation ' ⁇ ' represents the concatenation operation.
  • the signature method may comprise a first key generation step E100 implemented by the key management server 203s, represented in FIG. Figure 4 .
  • the processing means of the management server generate for the group a set of public parameters gpk and a group secret ⁇ .
  • the management server randomly determines a domain parameter dpk j and transmits it during a step E103 via its interface means to the server of the service provider SP j 204 belonging to a domain D j .
  • the public parameters gpk are made public during a step E104.
  • the domain parameter dpk j is also made public.
  • the group secret is thus not part of the gpk public parameters, and is held only by the managing authority.
  • the difficulty in implementing the discrete logarithm algorithm for a well-chosen group G 2 makes it possible to guarantee the practical impossibility of finding the group secret ⁇ from w.
  • the distribution of w in the set of public parameters gpk does not pose any security problem of the signature mechanism and w will be used to check the group membership of the signer of a message.
  • the key management server For each service provider SP j , the key management server generates a domain parameter dpk j , specific to the domain D j .
  • This parameter can be a function of an integer r j .
  • this parameter can be equal to g 1 r j .
  • the integer r j may advantageously be generated randomly by the management server using its cryptographic unit. The The management server then transmits this parameter via its interface means to the server of the service provider SP j .
  • the public parameters gpk and, if applicable, the domain parameter dpk j can be made public in various ways. They can be sent to user devices 201 and 205s control servers by service providers or published on a service provider site.
  • the signature method may also comprise, according to one embodiment of the invention, a second group membership step E200 of creating a secret signature key for a new member adhering to the group, described in FIG. Figure 5 .
  • This step can be implemented when a holder of a user device 201 wishes to become a member M i , i integer, of the group managed by the key management authority 203 acting as the group manager.
  • this member can generate during a step E201 using the processing means of its portable electronic device a first key portion unknown to the key management authority, transmit during a step E203 an identity data item, computed during a step E202 by these processing means from this first key part, to the key management server 203s and prove to the key management authority with the help of this identity data that it holds the first key part by a Zero Knowledge proof algorithm.
  • the key management server then generates during a step E204 and then transmits to the member M i during a step E205 the missing key part forming with the first key part the signature key of the member M i .
  • Ai which constitutes the third key part is a function of the group secret and allows the member to prove that he is part of the group.
  • the member M i is the only one to know the entirety of its signature key consisting of the first, second and third key parts. None, not even the key management authority can therefore sign a message instead of the member.
  • the signature key of the member M i may be stored in secure storage means of the user device belonging to the member M i , advantageously in the non-volatile memory of the corresponding portable electronic device.
  • the second and third key portions can be stored by the key management server, advantageously within a database stored in the storage means of the key management server or connected thereto.
  • the first key portion fi is calculated from a biometric data of the member M i captured by the sensors of the portable electronic device or stored therein.
  • the first key portion f i may also be the result of the application by the processing means of the portable electronic device of a hash function to such biometric data.
  • the managing authority when performing this step of joining a group, sends the result of the coupling e (A i , g 2 ) to the member M i to avoid that it has to take in charge the computation of a coupling later during the computation of the signature.
  • the signature method comprises a third step E300 of signature of a message m, described in FIG. Figure 6 .
  • the message m can be a challenge ("challenge") previously transmitted by a control server 205s to the member M i or any type of message to be signed by the member M i .
  • the domain parameter dpkj is also transmitted to the member Mi, if the latter has not been made public or is not already known to said member.
  • This step makes it possible to generate, during a step E301 for the message m, a group signature making it possible to prove membership of the member to the group anonymously and to associate therein during a step E302 a pseudonym nym ij identifying the member M i .
  • Said pseudonym and said signature are a function of a part of said secret signature key of the member M i , and are constructed so as to prove that the member identified by the pseudonym is the signatory of the message m.
  • said pseudonym nym ij of the member M i is specific to the domain D j .
  • the processing means of the user device implement a proof algorithm with zero disclosure of knowledge in which the signature is generated so as to prove that the member identified by the pseudonym nym ij is the signatory of the message m.
  • the elements B, J, K, T c, s f, s x, s a and s b signature can be used to verify membership in the group member independently of the pseudonym. The signature can therefore be used anonymously.
  • the pseudonym and the elements B, K, d and s x2 of the signature can be used to prove that the same secret key was used to generate the pseudonym and the signature, and thus prove that the member identified by the pseudonym nym ij is the signatory of the message m.
  • the signature ⁇ and the element R 5 can be used to check the membership of the member to the group independently of the pseudonym, and therefore anonymously.
  • the signature and the pseudonym can be used to prove that the member identified by the pseudonym nym ij is the signatory of the message m.
  • the signature and the pseudonym can be used to prove in a single verification operation the membership of the member to the group and that the member identified by the pseudonym nym ij is the signatory of the message m, as detailed below.
  • the pseudonym of the member M i in the domain D j being formed from the domain parameter dpk j specific to the domain Dj, the member M i will have different pseudonyms in different domains. It is then impossible for service providers 204 or verifiers 205 to determine whether two messages in two different domains with different signatures and pseudonyms have been signed by the same member ("cross-domain unlinkability").
  • xi which constitutes a second secret signature key portion, is used both for calculating the signature of the message m and for generating the pseudonym used by the member M i .
  • the management authority 203 can send, when the group membership step E200 is executed, the result of the coupling e (A i , g 2 ) to the member M i so that the latter does not have to take charge of calculating this coupling when calculating R 3 .
  • e T 2 boy Wut 2 e AT i boy Wut 2 e boy Wut ⁇ 1 boy Wut 2 at . Knowing e (A i , g 2 ) and the member M i no longer has exponentiations and multiplications to calculate.
  • all the calculations carried out during this signature step can be performed offline before receiving the message m to be signed, with the exception of the hash calculation and the exponentiations of R 5 and nym ij .
  • the user device 201 of the member Mi transmits during a step E303 by its communication interface means the signature ⁇ obtained, the pseudonym corresponding to the member M i , and the element R 5 in the second embodiment, the 205s control server that sent him the challenge to sign, or the recipient of the message m to which he also sends the message m.
  • the invention also relates to a signature and signature control method, an embodiment of which is described in Figure 7 and which may comprise steps of creating an E400 revocation database, a step E500 of implementing the signature method illustrated in FIG. Figure 3 and a signature control step E600, steps E400 and E600 being described below.
  • a revocation mechanism can be implemented in step E400.
  • a revocation list can be established for each domain and updated by the managing authority 203.
  • a revocation list RL j for the domain Dj is constructed from the pseudonyms nym ij of members of the revoked group and stored in a revocation database BD j .
  • the management server 203s transmits to each server 204s of the service provider SP j , the second secret key portion x i of the member, and each server of the service provider SP j calculates the corresponding nym ij nicknames and adds them in the revocation list RL j of the revocation database BD j .
  • said verification step comprises a proof verification step in which the control server processing means verifies that a zero-proof proof of knowledge proving that the member identified by the pseudonym is the signatory of the message (m) is correct.
  • the membership of the signatory to the group is verifiable independently of the pseudonym and the verification that the proof that the member identified by the pseudonym is the signer of the message is correct is carried out by separate operations from the signature and the pseudonym.
  • said verification step may comprise a verification operation of said signature making it possible to prove both the membership of the member (Mi) to the group and that the member identified by the pseudonym is the signatory of the message.
  • the control method E600 may also include a second revocation check step E602 of verifying that the member Mi has not been revoked from the group.
  • a verifier can control the membership of the signatory of the message to the group without knowing the group secret and identify the signatory by his pseudonym.
  • the verifier can also check that the pseudonym provided with the signature identifies the signatory.
  • control server processing means check in the revocation database BD j that the pseudonym nym ij does not belong to the revocation list RL j .
  • the control server To check the signature of a message m and the pseudonym of the member M i , the control server only needs to know this signature and this pseudonym as well as the domain parameters dpk j and the public parameters gpk. In particular, the control server is not aware of the secret signature key of the member M i . No control server can therefore sign a message instead of the member, nor know the pseudonym of the member M i in several areas and connect the signatures and pseudonyms of this member for different domains. Thus, and by the construction of pseudonyms: when we observe two pseudonyms for two different domains, it is impossible, thanks to hypotheses of complexity of certain mathematical problems, to say whether they correspond or not to the same member.
  • the revocation list is not taken into account when signing. This eliminates the need to renew valid member keys after a member revocation and does not involve additional calculations for the signer.
  • control server processing means only have a list membership test to be performed and not a linear number of arithmetic operations as in the signature mechanisms of the control server. group known.
  • valid membership lists are used instead of revocation lists.
  • the control server must then verify that the pseudonym that it verifies belongs to the list of valid members.
  • the storage databases of these lists are stored on the servers of the service providers.
  • the lists are stored in a common database stored on the key management server.
  • the object of the invention makes it possible to construct signatures using pseudonyms and allowing a member of a group to sign a message on behalf of the group, while having an identity in the group, without presenting the disadvantages of the mechanisms of the group. signature using pseudonyms.
  • the signature mechanism that is the subject of the invention can be applied to produce, for example, anonymous biometric authentications as described in the reference Bringer, J. Chabanne, H. Pointcheval, D. Zimmer, S. An application of the Boneh and Shacham group signature scheme to biometric authentication.
  • Springer (2008 ) and can be based on "Backward Unlinkability" group signatures as described in the reference Bringer, J., Patey, A. VLR group signatures - how to achieve both backward unlinkability and efficient revocation checks.
  • SECRYPT pp.

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Claims (14)

  1. Signaturverfahren einer Nachricht (m), umgesetzt von Verarbeitungsmitteln einer Benutzervorrichtung eines zu einer Mitgliedergruppe (
    Figure imgb0029
    ), die von einer Schlüsselverwaltungsautorität verwaltet wird, gehörenden Mitglieds (Mi), wobei die Benutzervorrichtung einen Geheimsignaturschlüssel (ski) besitzt,
    umfassend einen Erzeugungsschritt (E301) für die Nachricht (m) einer Gruppensignatur (σ), die es dem Mitglied (Mi) ermöglicht, seine Zugehörigkeit zur Mitgliedergruppe (
    Figure imgb0029
    ) zu beweisen, und einen Erzeugungsschritt (E302) eines Pseudonyms (nymij), welches das Mitglied (Mi) in einem Bereich (Dj) eines Diensteanbieters (SPj) identifiziert, wobei der Bereich eine Gruppe von Kommunikationsterminalen mit einem Server des Diensteanbieters umfasst,
    wobei die Gruppensignatur (σ) derart konstruiert ist, dass das Mitglied (Mi) bei Unterzeichnung der Nachricht (m) seine Kenntnis des Geheimsignaturschlüssels beweisen kann, ohne ihn zu offenbaren,
    und dadurch gekennzeichnet, dass die Gruppensignatur (σ) derart konstruiert ist, dass die Zugehörigkeit des Mitglieds (Mi) zur Gruppe unabhängig vom Pseudonym (nymij) verfifizierbar ist,
    und dass der Geheimsignaturschlüssel (ski) des Mitglieds (Mi) mindestens einen ersten Schlüsselteil (fi), der von den Verarbeitungsmitteln der Benutzervorrichtung des Mitglieds verwaltet wird und der Schlüsselverwaltungsautorität unbekannt ist, umfasst,
    und das Pseudonym und die Signatur von einem zweiten Teil (xi) des Geheimsignaturschlüssels des Mitglieds (Mi) abhängen und derart konstruiert sind, um zu beweisen, dass das von dem Pseudonym identifizierte Mitglied der Unterzeichner der Nachricht (m) ist,
    und dass das Pseudonym (nymij) des Mitglieds (Mi) für den Bereich (Dj ) spezifisch ist.
  2. Signaturverfahren nach vorangehendem Anspruch, dadurch gekennzeichnet, dass der Geheimsignaturschlüssel (ski) in einem abgesicherten Speichermittel gespeichert ist.
  3. Signaturverfahren nach einem der vorangehenden Ansprüche, dadurch gekennzeichnet, dass vor den Schritten der Erzeugung einer Gruppensignatur und eines Pseudonyms das Verfahren einen Schlüsselerzeugungsschritt (E100) umfasst, der von einem Schlüsselerzeugungsserver der Schlüsselverwaltungsautorität umgesetzt wird, bei dem Verarbeitungsmitteln des Verwaltungsservers:
    - für die Mitgliedergruppe (
    Figure imgb0029
    ) eine Gruppe öffentlicher Parameter (gpk) (E101) generieren,
    - einen Bereichsparameter (dpkj) bestimmen, der spezifisch für den Bereich (Dj) (E102) ist, und,
    - diesen Parameter an den Diensteanbieter (SPj) (E103) übertragen.
  4. Signaturverfahren nach Anspruch 3, dadurch gekennzeichnet, dass der Bereichsparameter (dpkj) gleich g 1 rj ist mit rj als Ganzzahl und g1 als Generator einer Gruppe G1, wobei g1 ein Parameter aus der Gruppe öffentlicher Parameter (gpk) ist.
  5. Signaturverfahren nach Anspruch 4, dadurch gekennzeichnet, dass die Ganzzahl rj von der Schlüsselverwaltungsautorität bestimmt wird.
  6. Signaturverfahren nach einem der Ansprüche 3 bis 5, dadurch gekennzeichnet, dass das Pseudonym (nymij) des Mitglieds (Mi) im Bereich (Dj) vom Bereichsparameter (dpkj) abhängt, der spezifisch für den vom Verwaltungsserver bestimmten Bereich (Dj) ist.
  7. Kontrollverfahren einer Signatur einer Nachricht (m) und eines Pseudonyms, das von Verarbeitungsmitteln eines Kontrollservers umgesetzt wird, wobei die Signatur (σ) und das Pseudonym (nymij) gemäß dem Verfahren nach einem der vorangehenden Ansprüche erzeugt (E500) werden,
    umfassend einen Überprüfungsschritt (E601) auf der Basis der Signatur (σ) und des Pseudonyms (nymij) der Kenntnis durch das Mitglied (Mi) des Geheimsignaturschlüssel (ski) und dass das Pseudonym und die Signatur des Mitglieds (Mi) von einem zweiten Teil (xi) des Geheimsignaturschlüssel abhängen, um zu beweisen, dass das durch das Pseudonym identifizierte Mitglied der Unterzeichner der Nachricht (m) ist und dass es zu der Mitgliedergruppe (
    Figure imgb0029
    ) gehört.
  8. Kontrollverfahren nach Anspruch 7, dadurch gekennzeichnet, dass der Überprüfungsschritt einen Beweisüberprüfungsschritt umfasst, bei dem die Verarbeitungsmittel des Kontrollservers überprüfen, dass ein Null-Offenbarungs-Kenntnisbeweis, der beweist, dass das durch das Pseudonym identifizierte Mitglied der Unterzeichner der Nachricht (m) ist, richtig ist.
  9. Kontrollverfahren nach Anspruch 8, dadurch gekennzeichnet, dass das Pseudonym (nymij) gleich dpkj xi ist mit xi als zweiter Teil des Geheimsignaturschlüssels des Mitglieds (Mi) und dpkj als ein Parameter des spezifischen Bereichs des Bereichs und dass Signatur (σ) einen Wert K umfasst, der sich vom Pseudonym (nymij) unterscheidet, der Form B^xi mit B als Element der Gruppe G1 und xi als zweiter Geheimsignaturschlüssel des Mitglieds (Mi) und dass der Beweisüberprüfungsschritt die Gleichheit der diskreten Logarithmen des Werts K in Bank B und des Pseudonyms nymij in Bank dpkj überprüft.
  10. Kontrollverfahren nach einem der Ansprüche 8 bis 9, dadurch gekennzeichnet, dass der Überprüfungsschritt eine Überprüfung der Signatur umfasst, um die Zugehörigkeit des Mitglieds (Mi) zur Gruppe zu beweisen und dass der Beweisüberprüfungsschritt bei der Überprüfung der Signatur durchgeführt wird.
  11. Rechnerprogramm, umfassend Programmcodeinstruktionen für die Ausführung der Schritte des Verfahrens nach einem der vorangehenden Ansprüche, wenn das Programm auf einem Rechner ausgeführt wird.
  12. Benutzervorrichtung (201), umfassend mindestens ein Speichermittel, ein Verarbeitungsmittel und eine Kommunikationsschnittstelle, dadurch gekennzeichnet, dass sie konfiguriert ist, um ein Verfahren nach einem der Ansprüche 1 bis 6 umzusetzen.
  13. Kontrollserver (205s), umfassend mindestens ein Speichermittel, ein Verarbeitungsmittel und eine Kommunikationsschnittstelle, dadurch gekennzeichnet, dass er konfiguriert ist, um ein Verfahren nach einem der Ansprüche 7 bis 10 umzusetzen.
  14. System, dadurch gekennzeichnet, dass es mindestens eine Benutzervorrichtung (201) nach Anspruch 12 und mindestens einen Kontrollserver (205s) nach Anspruch 13 umfasst.
EP14712007.5A 2013-03-25 2014-03-25 Gruppensignatur unter verwendung eines pseudonyms Active EP2891268B1 (de)

Applications Claiming Priority (2)

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FR1352650A FR3003713B1 (fr) 2013-03-25 2013-03-25 Signature de groupe utilisant un pseudonyme
PCT/EP2014/055969 WO2014154694A1 (fr) 2013-03-25 2014-03-25 Signature de groupe utilisant un pseudonyme

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WO2018083327A1 (en) * 2016-11-07 2018-05-11 Telefonaktiebolaget Lm Ericsson (Publ) Mission-critical push-to-talk
FR3091107A1 (fr) * 2018-12-24 2020-06-26 Orange Procédé et système de génération de clés pour un schéma de signatures anonymes
US11283623B1 (en) 2019-06-03 2022-03-22 Wells Fargo Bank, N.A. Systems and methods of using group functions certificate extension
KR102372718B1 (ko) 2019-11-05 2022-03-11 한국전자통신연구원 발행인 익명성 인증서 시스템을 위한 분산화된 그룹 서명 방법
US11483162B1 (en) 2019-12-18 2022-10-25 Wells Fargo Bank, N.A. Security settlement using group signatures
US11398916B1 (en) 2019-12-18 2022-07-26 Wells Fargo Bank, N.A. Systems and methods of group signature management with consensus
US11265176B1 (en) 2019-12-18 2022-03-01 Wells Fargo Bank, N.A. Systems and applications to provide anonymous feedback
CN115379418B (zh) * 2022-08-19 2023-05-09 扬州大学 一种适用于车载自组网安全通信和条件隐私保护认证方法

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FR2834403B1 (fr) * 2001-12-27 2004-02-06 France Telecom Systeme cryptographique de signature de groupe
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EP2891268A1 (de) 2015-07-08
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US20160013946A1 (en) 2016-01-14
CA2895189C (fr) 2021-01-26
US9860069B2 (en) 2018-01-02
WO2014154694A1 (fr) 2014-10-02
FR3003713B1 (fr) 2016-10-07
IL240539A0 (en) 2015-10-29
CA2895189A1 (fr) 2014-10-02
FR3003713A1 (fr) 2014-09-26

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